Q.

z1  and z2  are the roots of z2+az+b=0  where a, b are non-zero complex numbers. It is known that the line joining the points A(z1) and B(z2)  pass through the origin, then a2/b is:

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a

Real

b

Purely imaginary

c

arg(a2/b)=π/4

d

None of these

answer is A.

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Detailed Solution

Line joining z1 and z2  passes through origin, therefore, z2=λz1 for some λ∈RWe have z1+z2=−a     ⇒(1+λ)z1=−aand z1z2=b   ⇒λz12=b∴    a2b=(1+λ)2z12λz12=(1+λ)2λ=real
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